A study of a country\'s colleges and universities resulted in the demand equatio
ID: 3311436 • Letter: A
Question
A study of a country's colleges and universities resulted in the demand equation q = 20,000 2p, where q is the enrollment at a public college or university and p is the average annual tuition (plus fees) it charges.† Officials at Enormous State University have developed a policy whereby the number of students it will accept per year at a tuition level of p dollars is given by q = 9,100 + 0.5p. Find the equilibrium tuition price p and the consumers' and producers' surpluses at this tuition level. What is the total social gain at the equilibrium price? HINT [See Example 3.] equilibrium tuition price p = $ consumers' surplus CS = $ producers' surplus PS = $ total social gain $
Explanation / Answer
Equilibrium tuition price= 4600
Social gain= 10800
Explanation:
20,000-2p=9100+0.5p
Collecting the like terms,
2.5p=10900
Therefore, p=4600 Hence, the equilibrium tuition price=4600
The social gain is in terms of student enrollment, thus q=20000-2*4600=10800 students
q=9500+0.5*4600=11800 students
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